Composite component manufacturing methods comprising a lay-up stage where layers of a composite material in a roll format are placed in a mould of suitable shape and a curing stage are well known in the aeronautical industry as well as in other industries.
The composite materials that are most used in the aeronautical industry consist of fibers or fiber bundles embedded in a matrix of thermosetting or thermoplastic resin, in the form of a preimpregnated or “prepreg” material. Their main advantages refer to:                Their high specific strength with respect to metallic materials.        Their excellent behavior under fatigue loads.        The possibilities of structural optimization thanks to the anisotropy of the material and the possibility of combining fibers with different orientations, allowing the design of the elements with different mechanical properties adjusted to the different needs in terms of applied loads.        
The layers of composite material are not placed randomly, but are arranged in each zone in a number and with an orientation of their fibre reinforcement, typically of carbon fibre, that depend on the nature and the magnitude of the stresses that are to be withstood by the component in each zone. Thus, each zone has a particular structure of the arrangement or stacking of the layers. The difference in thickness between the different zones generates drop-offs in the layers, which requires having a ply model for each component establishing how to the arrange the layers on the jig during the stacking process.
The lay-up stage is usually carried out using Automatic Tape Laying machines (hereinafter ATL machines) for laying unidirectional (UD) or fabric tapes. The tapes are laid directly upon a mould according to the shape of the component with its reinforcing fibers in the orientation established by the designer. The ATL machine shall then be provided with the trajectories to be followed for laying up the tapes of the composite material (usually CFRP prepeg).
The trajectories for the tapes in the 0° direction in a contoured surface shall desirably follow a “natural path” understanding for that a path in which the tape will follow the contoured surface without stretching or puckering while being laid.
The determination of said “natural path” for non-planar surfaces is however difficult.
In a first approach it was proposed to determine the trajectories for the tapes in the 0° direction as geodesic curves (i.e. curves which are locally straight with respect to the surface because its geodesic curvature is equal to zero at every point) but it was found that this trajectories involve excessive gaps between adjacent tapes of the typical dimensions used in the industry.
US 2006/0073309 disclose a method for calculating trajectories for the tapes in the 0° direction that avoid said excessive gaps and also the production of wrinkles on the tapes as a trajectory defined by a plurality of natural path segments, each of them defining a non-natural angle relative to adjacent segments of the path so that a transverse edge of each tape is disposed within a predetermined offset distance interval from an adjacent tape. The implementation of this method for large composite parts of a complex geometry such as aircraft wing skins having a double curvature involves computing problems and does not assure the absence of wrinkles.
It would be thus desirable a laying-up method where said desired trajectories could be easily calculated and provided to the ATL machine.